1. 1 Urban and ecosystem dynamics: past, present, future Douglas White 1-23-07 Workshop on aspects of Social and Socio-Environmental Dynamics School of Human Evolution and Social Change and Center for Social Dynamics and Complexity

2. 2 Thanks to Laurent Tambayong, UC Irvine Nataša Kejžar, U Ljubljana Constantino Tsallis, Ernesto Borges, Centro Brasileiro de Pesquisas Fısicas, Rio de Janeiro Peter Turchin, U Conn Céline Rozenblat, U Zurich Numerous ISCOM project and members, including Denise Pumain, Sander v.d. Leeuw, Luis Bettencourt Commentators Michael Batty, William Thompson, George Modelski

3. 3 Outline Measure for city size deviations from Zipfian constructed and fitted to three Eurasian world regions. Does the shape parameter q of these distributions oscillate historically in longer periods than expected at random? Does fall in q away from Zipfian correlate with other measures of instability, e.g., internecine warfare or sociopolitical violence? Do variations in shape parameter q represent alternating periods of stability and instability?  Are city distributions historically unstable, as argued by Michael Batty, Nature 2006, (citing White et al. 2005) Does shape parameter q for China affect Europe q with a time lag (diffusion of innovation, Silk Route trade)?  Do city size instabilities affect world- system centers?

4. 4 Michael Batty (Nature, Dec 2006:592), using some of the same data as do we for historical cities (Chandler 1987), states the case made here: Batty shows legions of cities in the top echelons of city rank being swept away as they are replaced by competitors, largely from other regions. “It is now clear that the evident macro-stability in such distributions” as urban rank-size hierarchies at different times “can mask a volatile and often turbulent micro-dynamics, in which objects can change their position or rank-order rapidly while their aggregate distribution appears quite stable….” Further, “Our results destroy any notion that rank-size scaling is universal… [they] show cities and civilizations rising and falling in size at many times and on many scales.”

5. 5 City Size Distributions for Measuring Departures from Zipf construct and measure the shapes of cumulative city size distributions for the n largest cities from 1st rank size S 1 to the smallest of size S n as a total population distribution T r for all people in cities of size S r or greater, where r=1,n is city rank Rank size power law M~S 1 Cumulative city- population distribution

6. 6 City Size Distributions for Measuring Departures from Zipf This typical form of the city-size distribution tends toward a power-law in the tail, with a crossover C where smaller city sizes tend more toward an exponential distribution. Rank size power law Cumulative city- population distribution

7. 7 City Size Distributions for Measuring Departures from Zipf This typical form of the city-size distribution tends toward a power-law in the tail, with a crossover C where smaller city sizes tend more toward an exponential distribution. This closely fits the q-exponential, Y q (S ≥ x) = Y0 (1-(1-q)x/κ) 1/(1-q) Rank size power law Cumulative city- population distribution

8. 8 City Size Distributions for Measuring Departures from Zipf The q-exponential, Y q (S ≥ x) = Y0 (1-(1-q)x/κ) 1/(1-q) asymptotes toward a power law in the tail when q>1, and levels at smaller city sizes toward a finite urban population Y0 as governed by a crossover parameter κ (kappa). Rank size power law Cumulative city- population distribution

9. 9 City Size Distributions for Measuring Departures from Zipf The q-exponential, Y q (S ≥ x) = Y0 (1-(1-q)x/κ) 1/(1-q) asymptotes toward a power law in the tail when q>1, and levels at smaller city sizes toward a finite urban population Y0 as governed by a crossover parameter κ (kappa). Rank size power law Cumulative city- population distribution Lower q steeper α in the tail

10. 10 City Size Distributions for Measuring Departures from Zipf The q-exponential, Y q (S ≥ x) = Y0 (1-(1-q)x/κ) 1/(1-q) asymptotes toward a power law in the tail when q>1, and levels at smaller city sizes toward a finite urban population Y0 as governed by a crossover parameter κ (kappa). Rank size power law Cumulative city- population distribution Higher q flatter α in the tail

11. 11 City Size Distributions for Measuring Departures from Zipf Rank size power law Cumulative city- population distribution Straight- line in semilog for Zipfian In shifting to a semilog rather than a log-log plot of T r in which the Zipfian is expressed as a straight line, we see that many of the empirical distributions in semilog are relatively Zipfian but some bow concavely from a straight line when α>1.

12. 12 City Size Distributions for Measuring Departures from Zipf Rank size power law Cumulative city- population distribution In shifting to a semilog rather than a log-log plot of T r in which the Zipfian is expressed as a straight line, we see that many other empirical distributions in semilog bow concavely from a straight line either when α>1 for a rank-size power-law, or when the q-exponential has a higher crossover. Bowed- line in semilog non- Zipfian

13. 13 City Size Distributions for Measuring Departures from Zipf q is usually 0 and China q leads Europe q by 50 years (diffusion time) Either way. Log-log or semilog, we carry out curve fitting to the q-exponential, Y q (S ≥ x) = Y0 (1-(1-q)x/κ) 1/(1-q) and do so with Chandler’s largest historical cities, 900-1970, for China, Europe, Middle Asia in between, and the Mideast.

14. 14 City Size Distributions for Measuring Departures from Zipf q is usually 0 and both China q and Europe q depress the Middle Asia q within 50 years (competition?) Middle Asia, caught between China and Europe as connected by the Silk Roads, has a different profile and interaction.

15. 15 China boosted by Middle Asia q

16. 16 Europe not boosted by Middle Asia q

17. 17 City Size Distributions as Measured by q Departures from Zipf are historically unstable: Middle Asia q is usually 0 and both China q and Europe q depress the Middle Asia q within 50 years (competition?)

18. 18 City Size Distributions as Measured by q Departures from Zipf are historically unstable: Europe q is usually ½ and China q leads Europe q by 50 years (diffusion time)

19. 19 City Size Distributions as Measured by q Departures from Zipf are historically unstable: China q is usually 0 and China q leads Europe q by 50 years (diffusion time)

20. 20 City Size Distributions as Measured by q Departures from Zipf are correlated with instability: China Chinese SPIm=Sociopolitical Instability (moving average) as measured by Internecine wars (Lee 1931), 25 year periods interpolated for q

21. 21 Conclusion Measure for deviations from Zipfian (q, kappa) constructed and fitted to three Eurasian world regions. Shape parameter q of these distributions oscillates historically in longer periods than expected at random (detrended kappa also). Fall in q away from Zipfian explored for China, found to be strongly correlated with internecine warfare, more generally SP Instability. Variations in shape parameter q represent periods of stability, instability  city distributions are historically unstable. Shape parameter q for China affects Europe q with 50 year lag (diffusion of innovation, Silk Route trade). China and Europe q affect Middle Asia q negatively (competition)  city size instabilities affect world-system centers.

22. 22 Implications Connect these results with those of Geoff West, Luis Bettencourt and Jose Lobo (Chapter 1, ISCOM book), showing the energetic inefficiency of larger cities. That, along with city system instabilities, has implications for more severe consequences as urban population systems grow in size. Energy inefficiencies that are cumulative, growing since the industrial revolution  severe global warming with no end in sight. This includes a 240-300 foot rise in oceans by 22 nd C., and flooding of huge number of coastal cities, displacing 10% or more of world population. Need to consider new design principles for redesigning cities that are energetically efficient in self sustaining local and global systems.

23. 23 Policy Research on Urban Redesign, Energy, and Ecosystem With a 240-300 foot rise in oceans by 22 nd C., and flooding of huge number of coastal cities, displacing 10% or more of world population and greater infrastructural efficiency energy inefficiencye of larger cities (and conversely for smaller cities), need to study redesign of new cities inland in the smaller range that are energetically efficient in self-sustaining local and global systems. Existing cities inland in the larger range that are energetically efficient and sustainable in global systems.

24. 24 Cohesive Info.Redesign, Minimum Energy, and Ecocoupling If the network hubs found in cities attract population, then membership in cohesive netgroups per capita might be lower in cities because of centralization, road design, and now, developer design of suburbs. In the era prior to developer design of segmentary suburbs (tree-like intaburb streets, aparteid in sociopolitical effects), ecological psychology found greater productive role density and satisfaction in smaller settlements. This could become a renewed design principle. Similarly, in large cities, cohesive designs could be tested against segmentary aparteid principles and used in design principles for energetic and ecological efficiencies and sustainabilities.

25. 25 Scaling Issues Good deal of time devoted to finding reliable and unbiased estimates of the q-exponential parameters. Excel solver can be used, solving a whole series of distributions at once. Spss /Analyze/Regression/Nonlinear can be used, one distribution at a time. We are testing a candidate model for unbiased MLE of the q-exponential. Current findings replicated by different fitting methods. Crucial problems: –Accuracy when there are relatively few cases –Accuracy and unbiased estimation when the lower-sized cities are missing –Consistency of results when there are fewer or greater top ranked cities. Examination of possible biases in historical distributions.

26. 26 Replication and Consistency Data for other continents beside China will be run against indices of sociopolitical instability. Some such data are available from Peter Turchin. Regional variability in q studied for China in relation to Turchin’s historical dynamic models. Questions of accuracy of total population data for China, possibly other regions. Tests of population peaks for China show predicted dynamic lags to changes in SPI indices. Consistency tests work for Y0 estimates < Total population, and give estimates of percentage urbanization that for China appear to improve on Chinese census estimates. The kappa crossover parameter plays a role in the dynamics. The Yq distribution is differentiable. Use of the derivative allows direct mapping into size-specific processes of urban demographic change.

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